Total Number of Stations = 10451
Starting in 2000 and continuing through 2018
Total Sapidus Caught was 5531
Overall Frequency of Occurrence was 16.1228591
Overall Mean Catch Crabs/Hectare: 0.199
Stations with no catch: 8766 / 10451 Stations or 83.88%
| Survey_Year | Stations | Missing Obs | % Occurrence | Mean Catch | SD | Overdispersed |
|---|---|---|---|---|---|---|
| 2000 | 497 | 0 | 0.1247485 | 0.1430723 | 0.7418709 | yes |
| 2001 | 423 | 0 | 0.1560284 | 0.3999519 | 2.5068184 | yes |
| 2002 | 516 | 0 | 0.2151163 | 0.3052766 | 1.4236905 | yes |
| 2003 | 486 | 0 | 0.2098765 | 0.3210508 | 1.2982149 | yes |
| 2004 | 445 | 0 | 0.1842697 | 0.2669802 | 1.1315465 | yes |
| 2005 | 431 | 0 | 0.3039443 | 0.7309055 | 4.4504559 | yes |
| 2006 | 398 | 0 | 0.2512563 | 0.2974087 | 1.2510404 | yes |
| 2007 | 403 | 0 | 0.2431762 | 0.3695068 | 2.1259831 | yes |
| 2008 | 598 | 0 | 0.1505017 | 0.0887166 | 0.2906761 | no |
| 2009 | 983 | 0 | 0.1576806 | 0.1372921 | 0.5387720 | yes |
| 2010 | 700 | 0 | 0.1571429 | 0.1408543 | 0.5082154 | yes |
| 2011 | 549 | 0 | 0.2021858 | 0.2321763 | 0.8469300 | yes |
| 2012 | 589 | 0 | 0.0916808 | 0.0595966 | 0.2344135 | no |
| 2013 | 506 | 0 | 0.0790514 | 0.0494838 | 0.2574674 | yes |
| 2014 | 685 | 0 | 0.1138686 | 0.1251746 | 1.2178975 | yes |
| 2015 | 700 | 0 | 0.1314286 | 0.1177831 | 0.5375021 | yes |
| 2016 | 548 | 0 | 0.1423358 | 0.1173202 | 0.4557866 | yes |
| 2017 | 603 | 0 | 0.1293532 | 0.1521905 | 0.6661890 | yes |
| 2018 | 391 | 0 | 0.1202046 | 0.0789907 | 0.3358133 | yes |
| StatZone | Stations | Missing Obs | % Occurrence | Mean Catch | SD | Overdispersed |
|---|---|---|---|---|---|---|
| 1 | 5 | 0 | 0.0000000 | 0.0000000 | 0.0000000 | no |
| 2 | 125 | 0 | 0.0160000 | 0.0047240 | 0.0371959 | no |
| 3 | 399 | 0 | 0.0100251 | 0.0028436 | 0.0283030 | no |
| 4 | 443 | 0 | 0.0067720 | 0.0037170 | 0.0492515 | no |
| 5 | 416 | 0 | 0.0072115 | 0.0026857 | 0.0333903 | no |
| 6 | 415 | 0 | 0.0000000 | 0.0000000 | 0.0000000 | no |
| 7 | 253 | 0 | 0.0118577 | 0.0044019 | 0.0423148 | no |
| 8 | 281 | 0 | 0.0533808 | 0.0596740 | 0.3968039 | yes |
| 9 | 199 | 0 | 0.0000000 | 0.0000000 | 0.0000000 | no |
| 10 | 190 | 0 | 0.0421053 | 0.0143626 | 0.0695699 | no |
| 11 | 1106 | 0 | 0.1672694 | 0.1723934 | 0.8055450 | yes |
| 12 | 55 | 0 | 0.1454545 | 0.1419970 | 0.4399969 | yes |
| 13 | 396 | 0 | 0.4065657 | 0.9149865 | 2.7089809 | yes |
| 14 | 724 | 0 | 0.2997238 | 0.3343395 | 1.1222703 | yes |
| 15 | 732 | 0 | 0.2786885 | 0.5402363 | 3.5939280 | yes |
| 16 | 810 | 0 | 0.2197531 | 0.2461144 | 1.1254532 | yes |
| 17 | 914 | 0 | 0.1991247 | 0.1726239 | 0.5750543 | yes |
| 18 | 769 | 0 | 0.2028609 | 0.1800542 | 0.6481025 | yes |
| 19 | 772 | 0 | 0.2059585 | 0.1991595 | 1.2096515 | yes |
| 20 | 783 | 0 | 0.1558110 | 0.1569738 | 1.2266493 | yes |
| 21 | 663 | 0 | 0.1131222 | 0.1336667 | 1.0744834 | yes |
| region | Stations | Missing Obs | % Occurrence | Mean Catch | SD | Overdispersed |
|---|---|---|---|---|---|---|
| Texas | 2987 | 0 | 0.1714094 | 0.1686456 | 1.0660434 | yes |
| Louisiana | 3577 | 0 | 0.2633492 | 0.3793627 | 2.0320024 | yes |
| MS Bight | 1351 | 0 | 0.1487787 | 0.1489310 | 0.7365881 | yes |
| Florida | 2536 | 0 | 0.0118297 | 0.0088214 | 0.1367223 | yes |
| region | Season | Stations | Missing Obs | % Occurrence | Mean Catch | SD | Overdispersed |
|---|---|---|---|---|---|---|---|
| Texas | Summer | 1559 | 0 | 0.2373316 | 0.2236771 | 0.9768701 | yes |
| Texas | Fall | 1428 | 0 | 0.0994398 | 0.1085657 | 1.1529185 | yes |
| Louisiana | Summer | 1855 | 0 | 0.3347709 | 0.5529719 | 2.6690359 | yes |
| Louisiana | Fall | 1722 | 0 | 0.1864111 | 0.1923446 | 0.9153126 | yes |
| MS Bight | Summer | 695 | 0 | 0.1899281 | 0.2180501 | 0.9777604 | yes |
| MS Bight | Fall | 656 | 0 | 0.1051829 | 0.0757027 | 0.3080248 | yes |
| Florida | Summer | 1570 | 0 | 0.0159236 | 0.0133319 | 0.1728732 | yes |
| Florida | Fall | 966 | 0 | 0.0051760 | 0.0014906 | 0.0206892 | no |
| Survey_Year | Season | Stations | Missing Obs | % Occurrence | Mean Catch | SD | Overdispersed |
|---|---|---|---|---|---|---|---|
| 2000 | Summer | 251 | 0 | 0.1872510 | 0.2421858 | 1.0033596 | yes |
| 2000 | Fall | 246 | 0 | 0.0609756 | 0.0419443 | 0.2580981 | yes |
| 2001 | Summer | 172 | 0 | 0.2383721 | 0.9058880 | 3.8750995 | yes |
| 2001 | Fall | 251 | 0 | 0.0996016 | 0.0532547 | 0.1990548 | no |
| 2002 | Summer | 258 | 0 | 0.2829457 | 0.4726460 | 1.9025609 | yes |
| 2002 | Fall | 258 | 0 | 0.1472868 | 0.1379073 | 0.6210433 | yes |
| 2003 | Summer | 206 | 0 | 0.3543689 | 0.4785203 | 1.2481802 | yes |
| 2003 | Fall | 280 | 0 | 0.1035714 | 0.2051983 | 1.3240994 | yes |
| 2004 | Summer | 252 | 0 | 0.2301587 | 0.3461199 | 1.3364643 | yes |
| 2004 | Fall | 193 | 0 | 0.1243523 | 0.1636476 | 0.7790789 | yes |
| 2005 | Summer | 179 | 0 | 0.3240223 | 1.2656170 | 6.6823714 | yes |
| 2005 | Fall | 252 | 0 | 0.2896825 | 0.3510905 | 1.3841155 | yes |
| 2006 | Summer | 235 | 0 | 0.3446809 | 0.4610205 | 1.5999632 | yes |
| 2006 | Fall | 163 | 0 | 0.1165644 | 0.0615268 | 0.2074697 | no |
| 2007 | Summer | 179 | 0 | 0.2793296 | 0.2644754 | 0.7826726 | yes |
| 2007 | Fall | 224 | 0 | 0.2142857 | 0.4534382 | 2.7645823 | yes |
| 2008 | Summer | 288 | 0 | 0.1250000 | 0.0768972 | 0.2739921 | no |
| 2008 | Fall | 310 | 0 | 0.1741935 | 0.0996972 | 0.3053934 | no |
| 2009 | Summer | 539 | 0 | 0.2393321 | 0.2250547 | 0.7041287 | yes |
| 2009 | Fall | 444 | 0 | 0.0585586 | 0.0307515 | 0.1434819 | no |
| 2010 | Summer | 386 | 0 | 0.2020725 | 0.2032538 | 0.6373493 | yes |
| 2010 | Fall | 314 | 0 | 0.1019108 | 0.0641468 | 0.2577660 | yes |
| 2011 | Summer | 329 | 0 | 0.2401216 | 0.2478884 | 0.6765975 | yes |
| 2011 | Fall | 220 | 0 | 0.1454545 | 0.2086794 | 1.0527617 | yes |
| 2012 | Summer | 391 | 0 | 0.1023018 | 0.0670658 | 0.2382140 | no |
| 2012 | Fall | 198 | 0 | 0.0707071 | 0.0448467 | 0.2265906 | yes |
| 2013 | Summer | 313 | 0 | 0.1118211 | 0.0704450 | 0.3082615 | yes |
| 2013 | Fall | 193 | 0 | 0.0259067 | 0.0154898 | 0.1343925 | yes |
| 2014 | Summer | 364 | 0 | 0.1236264 | 0.1727832 | 1.6472389 | yes |
| 2014 | Fall | 321 | 0 | 0.1028037 | 0.0711885 | 0.2949376 | yes |
| 2015 | Summer | 377 | 0 | 0.1803714 | 0.1644393 | 0.5735665 | yes |
| 2015 | Fall | 323 | 0 | 0.0743034 | 0.0633268 | 0.4873321 | yes |
| 2016 | Summer | 354 | 0 | 0.1638418 | 0.1475319 | 0.5221085 | yes |
| 2016 | Fall | 194 | 0 | 0.1030928 | 0.0621916 | 0.2923462 | yes |
| 2017 | Summer | 322 | 0 | 0.1987578 | 0.2661089 | 0.8896509 | yes |
| 2017 | Fall | 281 | 0 | 0.0498221 | 0.0216505 | 0.1216030 | no |
| 2018 | Summer | 284 | 0 | 0.1232394 | 0.0910192 | 0.3813359 | yes |
| 2018 | Fall | 107 | 0 | 0.1121495 | 0.0470648 | 0.1589276 | no |
This model uses crabs per hectare as the response over the period of 18 years (2000-2018). Data is limited to statzones that were consistently sampled over the time period (i.e. West of Mobile Bay).
Model is a generalized linear model with a negative binomial error distribution. Blue crab catch is predicted as the sum of linear predictors for the year and season when the station was sampled in addition to the region in which it took place, with an interaction between survey year and region. An offset of area towed in hectares was used to predict catch as a rate and account for differences in sampling effort at different stations.
Looking at an interaction plot indicates that the impact of each region is not consistent across years and that there is an important interaction in the data.
Understanding p-values in glm model summary. Using the default settings in R sets the contrast levels for factors such that all factors are contrasted against the first/lowest factor level.
For example in our model year is modeled as a factor, which adjusts the intercept for the model for each. The first year is 2000, so all other years are contrasted against that year’s mean estimate. One quick way to confirm what factor level is the contrast is y checking which levels are absent from the summary table summary(my_model)
Contrasts:
year = 2000
region = texas
season = summer
P-values on factor levels in these tables indicate significant deviation from the contrasts. Post-hoc tests are necessary to compare individual levels against one another.
| term | estimate | std.error | statistic | p.value | signif. |
|---|---|---|---|---|---|
| (Intercept) | -2.6733145 | 0.2861883 | -9.3411033 | 0.0000000 | * |
| year_f2001 | 1.0514664 | 0.3885198 | 2.7063389 | 0.0068030 | * |
| year_f2002 | 1.1109845 | 0.3641262 | 3.0510975 | 0.0022801 | * |
| year_f2003 | 1.6181556 | 0.3560574 | 4.5446484 | 0.0000055 | * |
| year_f2004 | 0.6019168 | 0.3800132 | 1.5839367 | 0.1132081 | |
| year_f2005 | 0.7490335 | 0.3767514 | 1.9881373 | 0.0467965 | * |
| year_f2006 | 0.9665631 | 0.3737927 | 2.5858266 | 0.0097146 | * |
| year_f2007 | 3.2133377 | 0.3577372 | 8.9823978 | 0.0000000 | * |
| year_f2008 | 0.5411915 | 0.3862421 | 1.4011717 | 0.1611627 | |
| year_f2009 | 0.4107633 | 0.3550392 | 1.1569522 | 0.2472919 | |
| year_f2010 | 1.3448689 | 0.3594471 | 3.7414936 | 0.0001829 | * |
| year_f2011 | 1.9049743 | 0.3591069 | 5.3047558 | 0.0000001 | * |
| year_f2012 | 0.3831549 | 0.4033193 | 0.9500038 | 0.3421103 | |
| year_f2013 | -0.7583901 | 0.5169107 | -1.4671588 | 0.1423329 | |
| year_f2014 | 1.7883269 | 0.3715749 | 4.8128305 | 0.0000015 | * |
| year_f2015 | 1.4152758 | 0.3734316 | 3.7899204 | 0.0001507 | * |
| year_f2016 | 1.8209074 | 0.3783259 | 4.8130653 | 0.0000015 | * |
| year_f2017 | 1.3163765 | 0.3764208 | 3.4970878 | 0.0004704 | * |
| year_f2018 | 0.6150347 | 0.4944077 | 1.2439828 | 0.2135059 | |
| regionLouisiana | 1.3025000 | 0.3484004 | 3.7385142 | 0.0001851 | * |
| regionMS Bight | 0.8634275 | 0.4531161 | 1.9055327 | 0.0567109 | |
| seasonFall | -1.1944466 | 0.0705304 | -16.9352084 | 0.0000000 | * |
| year_f2001:regionLouisiana | 0.1648747 | 0.4780710 | 0.3448749 | 0.7301884 | |
| year_f2002:regionLouisiana | 0.0257097 | 0.4510884 | 0.0569948 | 0.9545493 | |
| year_f2003:regionLouisiana | -0.1879177 | 0.4552947 | -0.4127387 | 0.6797981 | |
| year_f2004:regionLouisiana | 0.4723590 | 0.4684591 | 1.0083250 | 0.3132985 | |
| year_f2005:regionLouisiana | 1.3939977 | 0.4643367 | 3.0021269 | 0.0026810 | * |
| year_f2006:regionLouisiana | -0.4545761 | 0.4857255 | -0.9358702 | 0.3493400 | |
| year_f2007:regionLouisiana | -2.7262074 | 0.4554546 | -5.9856840 | 0.0000000 | * |
| year_f2008:regionLouisiana | -0.3052659 | 0.4713490 | -0.6476431 | 0.5172158 | |
| year_f2009:regionLouisiana | -0.3030983 | 0.4413966 | -0.6866801 | 0.4922844 | |
| year_f2010:regionLouisiana | -0.8449438 | 0.4556076 | -1.8545429 | 0.0636615 | |
| year_f2011:regionLouisiana | -0.7890426 | 0.4562994 | -1.7292214 | 0.0837695 | |
| year_f2012:regionLouisiana | -0.6385626 | 0.5102218 | -1.2515391 | 0.2107378 | |
| year_f2013:regionLouisiana | 0.3367814 | 0.6155953 | 0.5470824 | 0.5843221 | |
| year_f2014:regionLouisiana | -1.3525118 | 0.4725849 | -2.8619450 | 0.0042105 | * |
| year_f2015:regionLouisiana | -0.8975941 | 0.4738916 | -1.8940917 | 0.0582128 | |
| year_f2016:regionLouisiana | -1.9674137 | 0.4845665 | -4.0601522 | 0.0000490 | * |
| year_f2017:regionLouisiana | -0.8602303 | 0.4816509 | -1.7860038 | 0.0740986 | |
| year_f2018:regionLouisiana | -0.3483886 | 0.6155945 | -0.5659385 | 0.5714356 | |
| year_f2001:regionMS Bight | -2.0061988 | 0.7065977 | -2.8392375 | 0.0045221 | * |
| year_f2002:regionMS Bight | -1.2985357 | 0.6222816 | -2.0867334 | 0.0369122 | * |
| year_f2003:regionMS Bight | -1.4933779 | 0.5899080 | -2.5315438 | 0.0113562 | * |
| year_f2004:regionMS Bight | -1.4073476 | 0.7022656 | -2.0040104 | 0.0450689 | * |
| year_f2005:regionMS Bight | 0.8046973 | 0.6279722 | 1.2814219 | 0.2000455 | |
| year_f2006:regionMS Bight | 0.2127872 | 0.5937276 | 0.3583920 | 0.7200500 | |
| year_f2007:regionMS Bight | -2.2032994 | 0.6443902 | -3.4192007 | 0.0006281 | * |
| year_f2008:regionMS Bight | -1.5333500 | 0.6880442 | -2.2285633 | 0.0258430 | * |
| year_f2009:regionMS Bight | 0.5905799 | 0.5645326 | 1.0461396 | 0.2954966 | |
| year_f2010:regionMS Bight | -0.7871644 | 0.7324190 | -1.0747460 | 0.2824884 | |
| year_f2011:regionMS Bight | -2.2660645 | 0.7769977 | -2.9164365 | 0.0035405 | * |
| year_f2012:regionMS Bight | -0.5864040 | 0.8119086 | -0.7222538 | 0.4701385 | |
| year_f2013:regionMS Bight | 0.5491646 | 0.9030651 | 0.6081119 | 0.5431133 | |
| year_f2014:regionMS Bight | -1.6589276 | 0.7381092 | -2.2475367 | 0.0246057 | * |
| year_f2015:regionMS Bight | -2.5392383 | 0.8707171 | -2.9162611 | 0.0035425 | * |
| year_f2016:regionMS Bight | -4.0973731 | 1.2419539 | -3.2991346 | 0.0009698 | * |
| year_f2017:regionMS Bight | -0.6909230 | 0.7147056 | -0.9667240 | 0.3336820 | |
| year_f2018:regionMS Bight | -0.5752396 | 0.9424485 | -0.6103671 | 0.5416187 |
| null.deviance | df.null | logLik | AIC | BIC | deviance | df.residual |
|---|---|---|---|---|---|---|
| 4729.793 | 7668 | -6694.188 | 13506.38 | 13916.13 | 3876.933 | 7611 |
Goodness of fit for generalized linear models is described using deviance. A glm will report 2 deviance measures:
null.deviance is the residual variation remaining from the null model. The null model here is the grand mean of blue crab catch per hectare of all observations
deviance is the residual variation remaining from the fitted model. Numbers closer to the null.deviance indicate that the model did not perform much better than the null model.
% deviance explained is calculated as \(\frac{null.deviance - deviance}{null.deviance} * 100\) and expresses the improvement of the fitted model over the null in % deviance explained.
Percent Deviance for model A. = 0.1803166
Significance of the entire factor can be obtained by using a Chi-squared likelihood ratio test.
| Predictor | Df | Deviance | AIC | LRT | Pr(>Chi) |
|---|---|---|---|---|---|
| NA | 3876.933 | 13504.38 | NA | NA | |
| year_f | 18 | 4110.423 | 13701.87 | 233.49003 | 0.0000000 |
| region | 2 | 3890.379 | 13513.82 | 13.44667 | 0.0012025 |
| year_f:region | 36 | 4101.267 | 13656.71 | 224.33463 | 0.0000000 |
Because we used area towed in the model as an offset predictions from our model can be interprated as crabs per hectare.
Model prediction (black) & observed mean values (blue)
This model uses crabs per hectare as the response over the period of 9 years (2009-2018). Data selection and sampling effort was consistent over this period. Additionally the survey expanded to the Eastern Gulf of Mexico so stat zones in that region are included as well.
Model is a generalized linear model with a negative binomial error distribution. Blue crab catch is predicted as the sum of linear predictors for the year and season when the station was sampled in addition to the region in which it took place, with an interaction between survey year and region. An offset of area towed in hectares was used to predict catch as a rate and account for differences in sampling effort at different stations.
Looking at an interaction plot indicates that the impact of each region is not consistent across years and that there is an important interaction in the data. The sharp peaks for Florida’s linear predictor reflect years when there was no catch.
| term | estimate | std.error | statistic | p.value | signif. |
|---|---|---|---|---|---|
| (Intercept) | -2.2365366 | 2.067740e-01 | -10.8163341 | 0.0000000 | * |
| year_f2010 | 0.9327593 | 2.919770e-01 | 3.1946332 | 0.0014001 | * |
| year_f2011 | 1.5017278 | 2.908812e-01 | 5.1626849 | 0.0000002 | * |
| year_f2012 | -0.0360237 | 3.428666e-01 | -0.1050662 | 0.9163233 | |
| year_f2013 | -1.1799056 | 4.695853e-01 | -2.5126542 | 0.0119827 | * |
| year_f2014 | 1.3797400 | 3.047361e-01 | 4.5276558 | 0.0000060 | * |
| year_f2015 | 1.0094688 | 3.072697e-01 | 3.2852861 | 0.0010188 | * |
| year_f2016 | 1.4121864 | 3.117953e-01 | 4.5292099 | 0.0000059 | * |
| year_f2017 | 0.9054476 | 3.109851e-01 | 2.9115463 | 0.0035964 | * |
| year_f2018 | 0.1784394 | 4.367306e-01 | 0.4085800 | 0.6828479 | |
| regionLouisiana | 0.9938844 | 2.604943e-01 | 3.8153789 | 0.0001360 | * |
| regionMS Bight | 1.1850534 | 3.016999e-01 | 3.9279207 | 0.0000857 | * |
| regionFlorida | -3.1051374 | 6.390040e-01 | -4.8593399 | 0.0000012 | * |
| seasonFall | -1.2678351 | 9.489630e-02 | -13.3602144 | 0.0000000 | * |
| year_f2010:regionLouisiana | -0.5304500 | 3.819282e-01 | -1.3888736 | 0.1648712 | |
| year_f2011:regionLouisiana | -0.4733305 | 3.815818e-01 | -1.2404432 | 0.2148115 | |
| year_f2012:regionLouisiana | -0.3245976 | 4.431647e-01 | -0.7324536 | 0.4638917 | |
| year_f2013:regionLouisiana | 0.6498545 | 5.586839e-01 | 1.1631880 | 0.2447532 | |
| year_f2014:regionLouisiana | -1.0345131 | 3.996120e-01 | -2.5887935 | 0.0096313 | * |
| year_f2015:regionLouisiana | -0.5877309 | 4.012382e-01 | -1.4647932 | 0.1429774 | |
| year_f2016:regionLouisiana | -1.6644446 | 4.127629e-01 | -4.0324475 | 0.0000552 | * |
| year_f2017:regionLouisiana | -0.5567964 | 4.100412e-01 | -1.3579035 | 0.1744943 | |
| year_f2018:regionLouisiana | -0.0201145 | 5.488016e-01 | -0.0366517 | 0.9707628 | |
| year_f2010:regionMS Bight | -1.5893384 | 5.405180e-01 | -2.9403987 | 0.0032779 | * |
| year_f2011:regionMS Bight | -2.8589086 | 6.214104e-01 | -4.6006775 | 0.0000042 | * |
| year_f2012:regionMS Bight | -0.8863818 | 6.369183e-01 | -1.3916726 | 0.1640216 | |
| year_f2013:regionMS Bight | -0.0560339 | 7.511082e-01 | -0.0746016 | 0.9405317 | |
| year_f2014:regionMS Bight | -2.2954727 | 5.915182e-01 | -3.8806457 | 0.0001042 | * |
| year_f2015:regionMS Bight | -3.2553797 | 7.383571e-01 | -4.4089504 | 0.0000104 | * |
| year_f2016:regionMS Bight | -4.8430972 | 1.143874e+00 | -4.2339435 | 0.0000230 | * |
| year_f2017:regionMS Bight | -1.4097640 | 5.574585e-01 | -2.5289129 | 0.0114416 | * |
| year_f2018:regionMS Bight | -1.3784774 | 7.625142e-01 | -1.8078056 | 0.0706368 | |
| year_f2010:regionFlorida | -1.2931811 | 9.800153e-01 | -1.3195519 | 0.1869847 | |
| year_f2011:regionFlorida | -1.2502857 | 9.088825e-01 | -1.3756297 | 0.1689363 | |
| year_f2012:regionFlorida | -24.8886629 | 8.605019e+04 | -0.0002892 | 0.9997692 | |
| year_f2013:regionFlorida | 2.6234020 | 8.394040e-01 | 3.1253150 | 0.0017761 | * |
| year_f2014:regionFlorida | -0.6072040 | 7.811682e-01 | -0.7773025 | 0.4369803 | |
| year_f2015:regionFlorida | 1.1462852 | 7.169613e-01 | 1.5988103 | 0.1098628 | |
| year_f2016:regionFlorida | -26.2510380 | 9.093251e+04 | -0.0002887 | 0.9997697 | |
| year_f2017:regionFlorida | 0.0346248 | 7.968898e-01 | 0.0434499 | 0.9653429 | |
| year_f2018:regionFlorida | 1.0195593 | 8.329089e-01 | 1.2240947 | 0.2209165 |
| null.deviance | df.null | logLik | AIC | BIC | deviance | df.residual |
|---|---|---|---|---|---|---|
| 3412.127 | 6230 | -3424.967 | 6933.935 | 7216.901 | 2183.195 | 6190 |
Goodness of fit for generalized linear models is described using deviance. A glm will report 2 deviance measures:
null.deviance is the residual variation remaining from the null model. The null model here is the grand mean of blue crab catch per hectare of all observations
deviance is the residual variation remaining from the fitted model. Numbers closer to the null.deviance indicate that the model did not perform much better than the null model.
% deviance explained is calculated as \(\frac{null.deviance - deviance}{null.deviance} * 100\) and expresses the improvement of the fitted model over the null in % deviance explained.
Percent Deviance for model B. = 0.3601659
| Predictor | Df | Deviance | AIC | LRT | Pr(>Chi) |
|---|---|---|---|---|---|
| NA | 2183.195 | 6931.935 | NA | NA | |
| year_f | 9 | 2261.870 | 6992.609 | 78.67436 | 0 |
| region | 3 | 2295.875 | 7038.615 | 112.68032 | 0 |
| year_f:region | 27 | 2327.365 | 7022.105 | 144.17031 | 0 |
Because we used area towed in the model as an offset predictions from our model can be interprated as crabs per hectare.
Model prediction (black) & observed mean values (blue)
The following numbers are from all usable data from 2000-2018
Total Number of Stations = 10395
Starting in 2000 and continuing through 2018
Total Sapidus Caught was 5515
Overall Frequency of Occurrence was 16.1327561
Overall Mean Catch Crabs/Hectare: 0.1997587
Stations with no catch: 8718 / 10395 Stations or 83.87%
The following numbers are from the Western Gulf Dataset used in the generalized linear model
Total Number of Stations = 7669
Starting in 2000 and continuing through 2018
Total Sapidus Caught was 5430
Overall Frequency of Occurrence was 21.3717564
Overall Mean Catch Crabs/Hectare: 0.267
Stations with no catch: 6030 / 7669 Stations or 78.63%
NOTE: Contains Data Across All Years and Regions (Including Florida)
| Survey Year | Stations | Missing Obs | % Occurrence | Mean Catch | SD | Overdispersed |
|---|---|---|---|---|---|---|
| 2000 | 491 | 0 | 0.1242363 | 0.1434330 | 0.7458628 | yes |
| 2001 | 416 | 0 | 0.1586538 | 0.4066819 | 2.5273291 | yes |
| 2002 | 514 | 0 | 0.2159533 | 0.3064645 | 1.4263351 | yes |
| 2003 | 478 | 0 | 0.2112971 | 0.3253341 | 1.3084392 | yes |
| 2004 | 440 | 0 | 0.1863636 | 0.2700141 | 1.1376114 | yes |
| 2005 | 430 | 0 | 0.3046512 | 0.7326053 | 4.4554998 | yes |
| 2006 | 393 | 0 | 0.2468193 | 0.2933579 | 1.2552633 | yes |
| 2007 | 401 | 0 | 0.2443890 | 0.3713497 | 2.1311305 | yes |
| 2008 | 596 | 0 | 0.1510067 | 0.0890143 | 0.2911187 | no |
| 2009 | 975 | 0 | 0.1569231 | 0.1354986 | 0.5365246 | yes |
| 2010 | 699 | 0 | 0.1573677 | 0.1410559 | 0.5085514 | yes |
| 2011 | 549 | 0 | 0.2021858 | 0.2321763 | 0.8469300 | yes |
| 2012 | 589 | 0 | 0.0916808 | 0.0595966 | 0.2344135 | no |
| 2013 | 503 | 0 | 0.0795229 | 0.0497789 | 0.2582070 | yes |
| 2014 | 684 | 0 | 0.1125731 | 0.1243615 | 1.2186026 | yes |
| 2015 | 696 | 0 | 0.1321839 | 0.1184600 | 0.5389722 | yes |
| 2016 | 547 | 0 | 0.1425960 | 0.1175347 | 0.4561761 | yes |
| 2017 | 603 | 0 | 0.1293532 | 0.1521905 | 0.6661890 | yes |
| 2018 | 391 | 0 | 0.1202046 | 0.0789907 | 0.3358133 | yes |
NOTE: Contains Data Across All Years and Regions (Including Florida)
NOTE 2: Mean Catch (per hectare) and frequency of occurrence calculated for each year, in each region, for each season. The mean and standard error of those annual measurements are then taken
NOTE 2: Mean Catch (per hectare) and frequency of occurrence calculated for each year, for each season. The mean and standard error of those annual measurements are then taken
| Formulation | AIC | Delta AIC |
|---|---|---|
| no interactions | 13649.41 | 143.030608 |
| year * region | 13506.38 | 0.000000 |
| year * season | 13547.85 | 41.477763 |
| region * season | 13650.10 | 143.728943 |
| all interactions | 13510.21 | 3.830144 |
| Predictor | Df | Deviance | AIC | LRT | Pr(>Chi) |
|---|---|---|---|---|---|
| NA | 3876.933 | 13504.38 | NA | NA | |
| year_f | 18 | 4110.423 | 13701.87 | 233.49003 | 0.0000000 |
| region | 2 | 3890.379 | 13513.82 | 13.44667 | 0.0012025 |
| season | 1 | 4129.406 | 13754.85 | 252.47388 | 0.0000000 |
| year_f:region | 36 | 4101.267 | 13656.71 | 224.33463 | 0.0000000 |
Percent Deviance Explained by Best Candidate Model: 18.03
Statistic reported below is the Wald Chi-Square z-score.
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | -2.6733145 | 0.2861883 | -9.3411033 | 0.0000000 |
| year_f2001 | 1.0514664 | 0.3885198 | 2.7063389 | 0.0068030 |
| year_f2002 | 1.1109845 | 0.3641262 | 3.0510975 | 0.0022801 |
| year_f2003 | 1.6181556 | 0.3560574 | 4.5446484 | 0.0000055 |
| year_f2004 | 0.6019168 | 0.3800132 | 1.5839367 | 0.1132081 |
| year_f2005 | 0.7490335 | 0.3767514 | 1.9881373 | 0.0467965 |
| year_f2006 | 0.9665631 | 0.3737927 | 2.5858266 | 0.0097146 |
| year_f2007 | 3.2133377 | 0.3577372 | 8.9823978 | 0.0000000 |
| year_f2008 | 0.5411915 | 0.3862421 | 1.4011717 | 0.1611627 |
| year_f2009 | 0.4107633 | 0.3550392 | 1.1569522 | 0.2472919 |
| year_f2010 | 1.3448689 | 0.3594471 | 3.7414936 | 0.0001829 |
| year_f2011 | 1.9049743 | 0.3591069 | 5.3047558 | 0.0000001 |
| year_f2012 | 0.3831549 | 0.4033193 | 0.9500038 | 0.3421103 |
| year_f2013 | -0.7583901 | 0.5169107 | -1.4671588 | 0.1423329 |
| year_f2014 | 1.7883269 | 0.3715749 | 4.8128305 | 0.0000015 |
| year_f2015 | 1.4152758 | 0.3734316 | 3.7899204 | 0.0001507 |
| year_f2016 | 1.8209074 | 0.3783259 | 4.8130653 | 0.0000015 |
| year_f2017 | 1.3163765 | 0.3764208 | 3.4970878 | 0.0004704 |
| year_f2018 | 0.6150347 | 0.4944077 | 1.2439828 | 0.2135059 |
| regionLouisiana | 1.3025000 | 0.3484004 | 3.7385142 | 0.0001851 |
| regionMS Bight | 0.8634275 | 0.4531161 | 1.9055327 | 0.0567109 |
| seasonFall | -1.1944466 | 0.0705304 | -16.9352084 | 0.0000000 |
| year_f2001:regionLouisiana | 0.1648747 | 0.4780710 | 0.3448749 | 0.7301884 |
| year_f2002:regionLouisiana | 0.0257097 | 0.4510884 | 0.0569948 | 0.9545493 |
| year_f2003:regionLouisiana | -0.1879177 | 0.4552947 | -0.4127387 | 0.6797981 |
| year_f2004:regionLouisiana | 0.4723590 | 0.4684591 | 1.0083250 | 0.3132985 |
| year_f2005:regionLouisiana | 1.3939977 | 0.4643367 | 3.0021269 | 0.0026810 |
| year_f2006:regionLouisiana | -0.4545761 | 0.4857255 | -0.9358702 | 0.3493400 |
| year_f2007:regionLouisiana | -2.7262074 | 0.4554546 | -5.9856840 | 0.0000000 |
| year_f2008:regionLouisiana | -0.3052659 | 0.4713490 | -0.6476431 | 0.5172158 |
| year_f2009:regionLouisiana | -0.3030983 | 0.4413966 | -0.6866801 | 0.4922844 |
| year_f2010:regionLouisiana | -0.8449438 | 0.4556076 | -1.8545429 | 0.0636615 |
| year_f2011:regionLouisiana | -0.7890426 | 0.4562994 | -1.7292214 | 0.0837695 |
| year_f2012:regionLouisiana | -0.6385626 | 0.5102218 | -1.2515391 | 0.2107378 |
| year_f2013:regionLouisiana | 0.3367814 | 0.6155953 | 0.5470824 | 0.5843221 |
| year_f2014:regionLouisiana | -1.3525118 | 0.4725849 | -2.8619450 | 0.0042105 |
| year_f2015:regionLouisiana | -0.8975941 | 0.4738916 | -1.8940917 | 0.0582128 |
| year_f2016:regionLouisiana | -1.9674137 | 0.4845665 | -4.0601522 | 0.0000490 |
| year_f2017:regionLouisiana | -0.8602303 | 0.4816509 | -1.7860038 | 0.0740986 |
| year_f2018:regionLouisiana | -0.3483886 | 0.6155945 | -0.5659385 | 0.5714356 |
| year_f2001:regionMS Bight | -2.0061988 | 0.7065977 | -2.8392375 | 0.0045221 |
| year_f2002:regionMS Bight | -1.2985357 | 0.6222816 | -2.0867334 | 0.0369122 |
| year_f2003:regionMS Bight | -1.4933779 | 0.5899080 | -2.5315438 | 0.0113562 |
| year_f2004:regionMS Bight | -1.4073476 | 0.7022656 | -2.0040104 | 0.0450689 |
| year_f2005:regionMS Bight | 0.8046973 | 0.6279722 | 1.2814219 | 0.2000455 |
| year_f2006:regionMS Bight | 0.2127872 | 0.5937276 | 0.3583920 | 0.7200500 |
| year_f2007:regionMS Bight | -2.2032994 | 0.6443902 | -3.4192007 | 0.0006281 |
| year_f2008:regionMS Bight | -1.5333500 | 0.6880442 | -2.2285633 | 0.0258430 |
| year_f2009:regionMS Bight | 0.5905799 | 0.5645326 | 1.0461396 | 0.2954966 |
| year_f2010:regionMS Bight | -0.7871644 | 0.7324190 | -1.0747460 | 0.2824884 |
| year_f2011:regionMS Bight | -2.2660645 | 0.7769977 | -2.9164365 | 0.0035405 |
| year_f2012:regionMS Bight | -0.5864040 | 0.8119086 | -0.7222538 | 0.4701385 |
| year_f2013:regionMS Bight | 0.5491646 | 0.9030651 | 0.6081119 | 0.5431133 |
| year_f2014:regionMS Bight | -1.6589276 | 0.7381092 | -2.2475367 | 0.0246057 |
| year_f2015:regionMS Bight | -2.5392383 | 0.8707171 | -2.9162611 | 0.0035425 |
| year_f2016:regionMS Bight | -4.0973731 | 1.2419539 | -3.2991346 | 0.0009698 |
| year_f2017:regionMS Bight | -0.6909230 | 0.7147056 | -0.9667240 | 0.3336820 |
| year_f2018:regionMS Bight | -0.5752396 | 0.9424485 | -0.6103671 | 0.5416187 |